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3 years ago

Which of the following has a graph that is a straight line?

Mathematics

1 answer:

Anit [1.1K]3 years ago

8 0

The answer is Equation 2: y = 5x - 4.5
it is a linear equation that the graph is a straight line

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Let $P$ and $Q$ be constants. The graphs of the lines $x + 5y = 7$ and $15x + Py = Q$ are perpendicular and intersect at the poi

Marta_Voda [28]

Answer:

(-3, -129)

Step-by-step explanation:

Given

Two lines:

$x + 5y = 7$

$15x + Py = Q$

are perpendicular to each other and intersect at point (-8,3).

To find: (P, Q)

Solution:

The two lines intersect at (-8,3).

It means, the equation of line will be satisfied when we put value of x = -8 and y = 3

Putting in the second equation, we will get an equation in P and Q:

$15\times (-8) + P \times 3 = Q\\\Rightarrow 3P = Q +120 ..... (1)$

Given that two lines are perpendicular.

It means the product of their slopes will be equal to -1.

i.e. $m_1\times m_2=-1$

Slope of a line of the form $ax+by+c=0$ is given as:

$m=-\dfrac{a}{b}$

So, slopes of given lines are:

$m_1=-\dfrac{1}{5}\\m_2=-\dfrac{15}{P}$

Using the condition:

$-\dfrac{1}{5}\times \dfrac{-15}{P}=-1\\\Rightarrow P = -3$

Putting the value of P in equation (1):

$\Rightarrow 3\times (-3) = Q +120 \\\Rightarrow Q = -9-120 = -129$

So, answer is (-3, -129)

7 0

3 years ago

If x- 3/4 =2 1/9 what does the x equals?

Romashka-Z-Leto [24]

3/4+-2 1/9=your ****ing answer

4 0

3 years ago

Which equation represents the equation of the parabola with focus (-3 3) and directrix y=7?

Artemon [7]

Answer:

The equation $y=\frac{-x^2-6x+31}{8}$ represents the equation of the parabola with focus (-3, 3) and directrix y = 7.

Step-by-step explanation:

To find the equation of the parabola with focus (-3, 3) and directrix y = 7. We start by assuming a general point on the parabola (x, y).

Using the distance formula $d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }$ , we find that the distance between (x, y) is

$\sqrt{(x+3)^2+(y-3)^2}$

and the distance between (x, y) and the directrix y = 7 is

$\sqrt{(y-7)^2}$ .

On the parabola, these distances are equal so, we solve for y:

$\sqrt{(x+3)^2+(y-3)^2}=\sqrt{(y-7)^2}\\\\\left(\sqrt{\left(x+3\right)^2+\left(y-3\right)^2}\right)^2=\left(\sqrt{\left(y-7\right)^2}\right)^2\\\\x^2+6x+y^2+18-6y=\left(y-7\right)^2\\\\x^2+6x+y^2+18-6y=y^2-14y+49\\\\y=\frac{-x^2-6x+31}{8}$

6 0

3 years ago

Felisa read the first 60 pages of a book in 3 days. She reads the last 90 pages in 6 days. Are these reading rates equivalent? E

Montano1993 [528]

No, because
60/3 = 20
90/6= 15
Both of the answers aren’t equivalent.

3 0

3 years ago

If f(x) = 3x - 9 and g(x) = x², what is (gºf)(5)?

Xelga [282]

Answer:

Step-by-step explanation:

Here, f(x) is the input to g(x), forming a composite function.

To evaluate (gºf)(5),

1) find the value of f(5). It is f(5) = 6.

2) Use this result as the input to g(x): g(6) = (6)^2 = 36

3 0

3 years ago